Question

v=at2+b÷t+c an equation find the dimensions and units of a,b,c​

Answer 1

Given :

A physical quantity is given by

• v = at² + b/t + c

» v denotes velocity

» t denotes times

» a, b & c are constants

To Find :

Dimensions and units of a, b and c.

Solution :

❒ Only like quantities having the same dimensions can be added to or substracted from each other$.$

We know that,

Dimension of velocity = [L¹T‾¹]

1. Dimension and unit of a :

➙ [v] = [a] [t]²

➙ [L¹T‾¹] = [a] [T¹]²

➙ [a] = [L¹T‾¹] / [T²]

➙ [a] = [L¹T‾³]

Unit of a will be m/s³

2. Dimension and unit of b :

➙ [v] = [b] / [t]

➙ [b] = [L¹T‾¹] [T¹]

➙ [b] = [L¹]

Unit of b will m

3. Dimension and unit of c :

➙ [v] = [c]

➙ [c] = [L¹T‾¹]

Unit of c will be m/s

Answer 2

Given :

A physical quantity is given by

v = at² + b/t + c

» v denotes velocity

» t denotes times

» a, b & c are constants

To Find :

Dimensions and units of a, b and c.

Solution :

❒ Only like quantities having the same dimensions can be added to or substracted from each other..

We know that,

Dimension of velocity = [L¹T‾¹]

1. Dimension and unit of a :

➙ [v] = [a] [t]²

➙ [L¹T‾¹] = [a] [T¹]²

➙ [a] = [L¹T‾¹] / [T²]

➙ [a] = [L¹T‾³]

Unit of a will be m/s³

2. Dimension and unit of b :

➙ [v] = [b] / [t]

➙ [b] = [L¹T‾¹] [T¹]

➙ [b] = [L¹]

Unit of b will m

3. Dimension and unit of c :

➙ [v] = [c]

➙ [c] = [L¹T‾¹]

Unit of c will be m/s